Saturday, March 18, 2006

Nancy Pearcey: The Creationists' Miss Information

I don't know about you, but whenever I want to learn about information theory, I naturally turn to the creationists. Why, they know so much about geology, biology, and paleontology, it only seems reasonable that their expertise would extend to mathematics and computer science.

Take Nancy Pearcey, for example. Here, for example, we learn that Ms. Pearcey has studied philosophy, German, and and music at Iowa State; that she has a master's degree in biblical studies; that she is a senior fellow at that temple of truth, the Discovery Institute; and that for nine years she worked with former Watergate conspirator and convicted criminal Charles Colson on his radio show, "Breakpoint". Why, those seem exactly the sort of credentials one would want in an instructor of information theory.

Infused with a thirst for knowledge, I headed immediately to my university's library to get her 1994 book co-written with Charles Thaxton, The Soul of Science: Christian Faith and Natural Philosophy. I didn't let the fact that it was donated by Trinity Missionary Church deter me; after all, this fine institution has donated other important books to our library, such as Larry Witham's By Design: Science and the Search for God.

The endorsements for The Soul of Science reassured me I was on the right track. David Shotton, a biologist at Oxford had this to say: "...the clarity of their explanations for the nonspecialist, for example, of Einstein's relativity theories or of the informational content of DNA and its consequences for theories of prebiotic evolution, are quite exceptional, alone making the volume worth purchasing." And there were equally enthusiastic endorsements from other experts in information theory, such as Phillip Johnson and Stephen Meyer.

I then turned to page 239. There I read the following explanation of information theory:

A structure with no order at all---for instance, a random set of letters---requires few instructions. If you want to write out a series of nonsense syllables, you need only two instructions: 1) "Select at random a letter of the English alphabet (or a space) and write it down," and 2) "Do it again." In the natural world a pile of leaves is random. It can be specified by saying 1) "Select at random some type of leaf --- oak, maple, birch --- and drop it on the pile," and 2) "Do it again." A random structure can be specified using few instructions. Hence it has a low information content.

Well, I think everyone would have to agree that this explanation is exceptionally clear and geared to the nonspecialist. Unfortunately, it is completely wrong.

According to information theory as elucidated by Kolmogorov, one does indeed measure the information content of a structure in terms of its shortest description. A string of a thousand A's "AAA.....A" has low information content because we can encode it as "Print A 1000 times". But it is a basic result of the theory -- so basic that I prove it in the very first class on Kolmogorov complexity at my university -- that a string of letters chosen uniformly at random has high information content, with very high probability. That's because such a random string is very unlikely to be generated by a simple program.

Where did Pearcey and Thaxton go wrong? They make two mistakes. First, although the procedure they suggest ("select at random a letter" and "do it again") indeed appears to be short, it does not constitute a description of a specific string. Run their procedure a second time, and you'd get a different string. Second, in Kolmogorov's theory, the description of a string must be completely deterministic; no "select at random" instructions are allowed. These are the kind of mistakes that could only be made by people completely unfamiliar with even the most basic aspects of information theory.

Of course, Pearcey and Thaxton aren't really interested in the information content of sentences or leaf piles. Their goal is to demonstrate that life is too complex to have evolved through natural means. But since high information content can result from random events -- for example, mutation -- it is not surprising at all that DNA can be viewed as a string with high Kolmogorov information. In fact, as Greg Chaitin has observed, pretty much the only way to get large amounts of information in the mathematical sense is to either do a really long calculation, or to exploit a source of randomness. DNA's high information content is prima facie evidence it resulted, in part, from an essentially random process.

So I left the library, disillusioned. How could the creationists be so wrong? Could they have allowed their personal religious beliefs to get in the way of their understanding? Or could they be deliberately misinforming the public to support their evangelical goals? No, the answer is clear: all the experts in information theory must be suppressing the truth.

Obviously, my classes on Kolmogorov complexity must take on a new aspect: teach the controversy!

42 comments:

Scott Belyea
said...

A useful and very clear post.

I have just one criticism ...

"... former Watergate burglar and convicted criminal Charles Colson on his radio show, "Breakpoint" "

What's the relevance? The answer, of course, is "none whatever." Just as it does not increase the credibility of a statement by pointing out that the speaker has a Ph.D. or is incredibly handsome, this sort of thing is irrelevant.

When a "creationist" mentions some real or imagined peccadillo of some scientist, defenders are quick to leap in to point out that 'even if true, the comment is irrelevant.' Same thing here.

You're speaking for the side with the evidence and the logic all to itself. Why resort to cheap tactics? It cannot help bolster your argument (which doesn't need bolstering), but it can distract from what you're saying.

After all, if a scientist whose work you admired were convicted of some criminal offence, would that lower your valuation of the work?

Jeff, I'm going to disagree with you on one point - DNA has no "information content as such. Our sequencing of DNA has information content because we can apply information metrics to it, but DNA itself is just a molecule that plays a particular crucial chemical role of catalysis in cells.

This is the distinction, if you like, between a UTM and a physical computer. You can't run a computer forever to see if a particular algorithm will halt. At best you can simulate it. UTMs are not physical things, and don't break down.

Likewise, DNA is not a sequence of symbols - it's a physical entity with structural as well as sequential properties, and our analyses of information content are just tools that may, or may not, give us abstract understanding of some of its properties in a given organism and environment.

When creationists use the word "information", they aren't really refering to the technical version of the word. Instead, I think they mean something more like "useful information" or "meaningful information". Random number generator isn't really creating any useful information. When viewed this way, their arguments make more sense. Unfortunately, they haven't recognized the fact that evolutionary forces (mutation, natural selection) can build new information.

But, my point is this: creationists are using a laypersons' version of information. Evolutionists must address the issue of meaningful information, not complain about the creationist's particular definition 'information'.

BC: if you read Pearcey and Thaxton's book, you will see that they definitely think they are using the standard mathematical meaning of information. On p. 239, for example, they quote Orgel defining information as "The minimum number of instructions needed to specify the structure", which is a reasonable, if informal, definition of Kolmogorov complexity. On page 240 they say "Information theory gives us a mathematical and conceptual tool for distinguishing between these two kinds of order..."

You're also wrong when you say that a random number generator doesn't generate useful information. That information is very useful if you're trying to find a quadratic nonresidue quickly, or test if a number is a prime.

I think it is a perfectly legitimate criticism to point out that creationists use the term "information" in a way that is contrary to the accepted mathematical definition of the term. I'd be perfectly happy to address the question of "meaningful information", if only I knew what the formal definition was.

" '... former Watergate burglar and convicted criminal Charles Colson on his radio show, 'Breakpoint' '

What's the relevance? The answer, of course, is 'none whatever.' "

It's not entirely irrelevent; in fact, in this case it is relevant in pointing out Colson's propensity for not being the straighforward and impartial participant in scientific inquiry that he is obviously claiming to be.

The point is that rather than being a scientist or an information theorist, Colson's claim to fame is as a conspiratorial purveyor of political misinformation on a national level.

The fact that he was convicted is valuable in driving home the point that questioning his honesty and truthfulness - and his political motive - is not without merit.

If he and a creationist team up and represent themselves as scientific authorities, how is the narrative of his previous career as a liar not entirely relevant?

"After all, if a scientist whose work you admired were convicted of some criminal offence, would that lower your valuation of the work?"

His WORK, no. Especially if it is actual repeatable science like it should be.

But it might make a difference for instance if there were concerns about that scientist's results, and if he was being investigated for faking results or making up data, and if his life was a morrass of dishonesty and obfuscation and criminal conviction of such.

However, your analagy is a little flawed because here we have an instance of a non-biologist claiming to enlighten the masses on biology and information theory.

Colson's conviction of being fast and loose with the facts for political purposes does go directly to the question of my valuation of his claims, which are in fact clearly political.

I agree that the definition of "meaningful information" is rather fuzzy. I'm not sure that I could come up with a good, general definition. Maybe "meaningful information" is only definable within a specific context. Here's an example of what I mean. Let's say that I want to genetically engineer an animal to run faster. Let's say that I want to add a new protein to the animal that will do this. There are a number of different proteins which could accomplish this - many of them working at different places within the animal's physiology. At the same time, the number of useful proteins (for accomplishing this) is a small fraction of all proteins that I could create. If I randomly generate a DNA sequence, it's highly unlikely to help the animal run faster - even though it contains a long, specific sequence of nucleotides. Despite the fact that the sequence contains "information" it's probably just junk that has no effect whatsoever on the animal. Two sequences might contain n nucleotides, but one is useless for the animal's movement rate, but the other helps it run faster. By the scientific definition of information, both sequences contain the same amount of information. But, in terms of "meaningful information" the first sequence has no value and the second has a lot of value. This is the differentiating line between "information" and "meaningful information".

Maybe that's a key point about meaningful information - it's only meaningful when attached to a specific context. So, if it's not possible to define "meaningful information" without also defining the context it exists within, maybe it's not possible to define "meaningful information" in any general (i.e. contextless) way. (Afterall, the sequence "ACGGCT" has no inherent usefulness unless you define the translation system and know the biology of the animal that will use the resulting protein; a different translation system or different animal might render the sequence useless.)

Scott, with due respect, the comments about Colson are relevant because Jeff Shallitt is drawing a comparison between Colson's history of lying for political advantage and Pearcey's lying for political advantage. Is it a smear by association? Well, yes, but the association isn't just that Pearcey knew Colson, but that she worked with him for years on a political radio show. Again, it is not unreasonable to point this out, especially as Jeff doesn't leave his criticism there but goes on to analyse the content of Pearcey's "work". And finally, you seem to think that making a mistake is not scientific. It is. When the error was pointed out, Jeff immedciately corrected the error. Do you want to take bets on when Pearcey will retract her flawed analysis now that the errors in it have been identified?

And to John: I disagree. A string of code like DNA has information content regardless of whether a human analyses it. While DNA is "just a molecule", it also true that DNA's "crucial chemical catalysis" relies completely on the sequence of its base pairs. The information content of the DNA is critical to its function, it isn't just a human construct.(from Chris Lawson)

Guys, the phrase you're groping for re: Colson is "ad hominem (circumstantial)": an attempt to argue against something about the person, not the person's argument. Both "former Watergate burglar" and "convicted criminal" refer to the person, not the truth or falsehood of the argument. Don in particular is mistaken in thinking that the trustworthiness of the speaker is valuable in evaluating what is really a mathematical statement: the truth or falsity of the statement stands on its own, without reference to the speaker.

“According to information theory as elucidated by Kolmogorov, one does indeed measure the information content of a structure in terms of its shortest description. ….. the description of a string must be completely deterministic;”

That is like saying “One does drink when they are thirsty but only that amount to quince their thirst.”

"When creationists use the word "information", they aren't really refering to the technical version of the word. Instead, I think they mean something more like "useful information" or "meaningful information"...But, my point is this: creationists are using a laypersons' version of information. Evolutionists must address the issue of meaningful information, not complain about the creationist's particular definition 'information'.# posted by BC : 1:52 PM...You are giving the creationists to much credit. They know exactly what they are doing; parading their ignorance as knowledge for the purpose of misinforming. Whether their ignorance is real or willfully counterfeit they are very well aware that they have nothing of value to say about a subject they know nothing about. While you are correct about what the creationists are doing, correcting the way they use 'information' is part of the solution. If laypeople wish to hold forth on a subject with scientists they must learn to give up their own 'laylanguage' and use the rigorously defined terms the scientists use. The never ending endeavor to make science understandable to laypeople in their own language has led the public to think they can take what they want of scientific language and leave the rest. This bad effect is where the creationist's wedge their deception. Showing how they are misusing the idea of 'meaningful information' when the phrase is not scientific anyway seems useful only to show the creationists deceitfullness.

Whether it's technically ad hominem or not - and it's not in my book - the point remains that Shallit's argument doesn't depend on Colson's history. That is, Shallitt doesn't make the argument, even implicitly, that "Colson is a liar, Pearcey worked with him and, therefore we can safely discount her book."

Actually, whenever we say something like "X, a researcher at Princeton has proposed...." then we are making a resort to authority. However, the work still has to stand on its own merits. It would be hard for science to function if, e.g., we didn't take some account of a person's status and track record.

The point being that adding some color to a post isn't the same thing as using that color to obscure the facts or misrepresent the situation. Typically creationists rely solely on ad hominem, resort to authority or straw men (as our beloved leader does too....).

Saying that Shallitt is making an ad hominem argument is the sort of political correctness that journalists use in reporting "both sides" without reference to the actual facts. Further, in this case the track record of these people is relevant and explains the egregious mistake they make in their definition of information, a mistake that many lay people make by the way.

You wrote in part: "But since high information content can result from random events -- for example, mutation." Other posters chimed in on the same point.

Can you tell me an inorganic process of the natural universe -- not a biological system or something created by a biological system -- that can create a code, along with an encoder mechanism and decoder mechanism that operate with that code?

If you want to write out a series of nonsense syllables, you need only two instructions: 1) "Select at random a letter of the English alphabet (or a space) and write it down," and 2) "Do it again."

So the string "bvc rd fgr jha" is composed of nonsense syllables? I don't think so. Those instructions are a bit too simple to produce the desired effect. You need to specify combining vowels and consonants if you want actual syllables.

While you are correct about what the creationists are doing, correcting the way they use 'information' is part of the solution. If laypeople wish to hold forth on a subject with scientists they must learn to give up their own 'laylanguage' and use the rigorously defined terms the scientists use.

The word "information" (meaning useful/meaningful information) may not be well defined or measurable, but it is still a valid concept. Both definitions are important. I don't think the solution is to get people to give up the non-scientific definition of the word. The non-scientific version of the word captures some concept that is not captured by the scientific version.

Let me put it this way: let's say that you find a book with all kinds of useful first-aid information. You read it and say, "gee, there's all this useful information about cleaning wounds, making a splint for broken bones..." You think, "Someone smart must've written this book because it's highly unlikely that random letters would form such useful information." Someone responds, "Well, my random letter generator creates information! A random generator is the very definition of an information generator! Information is a meansurable quantity that is related to the compressibility of the information." Of course, you would probably just roll your eyes because your definition of information (meaning the useful information contained in the book) isn't likely to be generated by a random letter generator. You know this no matter how hard someone tries to tell you about Shannon information theory and all that. You simply know that someone must've written the book -- despite all this talk about random letter generators and the creation of information.

I think it's similar to what some evolutionists are trying to do here. They're trying to convince people about this scientific definition of "information" which is not quite the same as the concept of useful information -- as if the information contained in a first-aid book is no different than the information created by a random letter generator. The solution is not to convince people to accept some new definition of information and throw out the old one. The fact of the matter is that evolution is quite capable of producing exactly the kind of information that the layperson is talking about (i.e. useful information). If you go the other direction and try to convince them to accept the scientific version of the word, they might very well realize that they're losing some important concept embodied in the idea of "useful information" versus "information". They might even think that evolutionists are doing some symantic slight-of-hand, reinforcing the whole ignorant "evolutionists are playing deceptive games" crap that gets so much play in creationist circles.

The fact of the matter is that evolution creates information (information in the sense that the layperson uses the word). That's the fact that has to be driven into the minds of the creationists.

" "Surely this isn't the "scientific" approach of "relevant and accurate data"?? :-)"

"If you can't attack the post, attack the author."

Well, this strikes me as somewhat odd, John. First, it was a closing comment with a smiley on it. Second, it "attacks" the "approach" and not the author. And third, if we really want to take my "criticism" seriously for a moment, 5 seconds to google "watergate burglars" tells you that there were 5 ... none of them Colson. Sloppy research, I say!! :-)

My point to start with was simply that I did not understand, given that all the facts and all the evidence are on your side of the "debate," why drag in "character" comments? I still don't understand ...

My point to start with was simply that I did not understand, given that all the facts and all the evidence are on your side of the "debate," why drag in "character" comments? I still don't understand ...

People on the "other side" of the "debate" (debate is enclosed in quotation-marks because there isn't a legitimate debate) are for the most part totally unwilling or unable to comprehend the facts and evidence. As a result, frustration on our side builds to the point that we drag in "character" issues.

Frankly, attempting to explain even the most rudimentary basics of information theory to your average ID creationist is rather like trying to teach calculus to a cow.

This isn't a dustup over issues in science. If it were, the discussion over the things creationists (Paleyists, scientific creationists, creation scientists, cdesign proponentsists, ID advocates, "teach the controversy" advocates, etc.) bring up would be recognized as having been addressed long, long ago, and the discussion would now be about other things.

But what is going on is a socio-political fight, as anti-science forces (the ones who use political processes to alter the definition of science, among other things) seek to get what they want, but can't establish via the mechanisms of science. As such, yeah, character is definitely something that deserves examination. I thought there was an issue of character over the falsehoods piled upon falsehoods in Henry Morris's "The Scientific Case for Creation". Others deserve to know about it, and not have it covered up by folks who claim that such is irrelevant to a discussion about the science. This isn't a discussion about the science; this is a discussion about the people who can't deal with the science and are out to cripple it by any means available.

So, for those who think that I, or others who work for the integrity of science education, should be muzzled concerning all the relevant information about the socio-political threats to science education, well, all I can say is that I'm not buying it, and I will continue to address both the content of the arguments (so far as there is content there), and also the issues of character that are surely relevant to understanding the complete picture.

On the subject of 'ad-hominem attacks' - the ID crowd lose no sleep over calling refering to Dawkins as an 'Atheist' which I understand is meant as an attack on his credibility in the US.This has no bearing on the weight of any scientific argument that he advances of course - and as ID has nothing to do with religion is completely irrelevant to the case.

Pointing out that someone has been found to be a liar and a perjurer in court is a useful factual piece of information when making a judgement of the credibility of an author. If someone plays fast and loose with their own credibility and gets found out, surely it's overstretching the principle of fair play to ignore the fact.

Judge Jones made some choice comments about Buckingham and others and their propensity to lie for their faith - does pointing out this fact constitute an 'ad hominem' attack on Buckingham, or is it merely restating the record?

A debater commits the Ad Hominem Fallacy when he introduces irrelevant personal premisses about his opponent.

I think that someone has been shown to be untruthful in court is not irrelevant in this case.

Pardon me if I am suspicious of your motives, but it's my experience that people who label their contributions as "just asking" are invariably creationist trolls who wrongly believe they are springing some irrefutable argument.

First, let's clarify what you mean by "code". To a mathematician, a code is a set of words S such that any word that can be written as a product of words in S only has one such representation. In other words, there is unique decipherability. Thus the set {a, ab} is a code, but {a, ab, ba} is not, since aba can be factored as (ab)(a) or (a)(ba).

Given that, is DNA a code? No, because codes are sets of words, and DNA is a molecule. When we interpret DNA as a string of symbols, that is our interpretation. Maybe the proper way to think of DNA is something entirely different, let's say, something involving topology.

But let's be charitable and interpret the question as meaning, can we view DNA as a code? Still hard to say, because it is not completely clear what the set of words is. Under some interpretations, DNA might not be a code, because frame-shifts can result in different readings.

But maybe you didn't mean this formal definition. Maybe by "code" you meant "information described in one form translated to another". That's hardly a precise definition, but I'll try to answer your challenge.

I'd say many things in nature can be viewed as encoding information provided in a different form. For example, varves and polar ice cores could be viewed as encoding yearly climate variation. Decoding is accomplished simply by shining light on an extracted layer of fossil sediment or ice, respectively.

But even if there were no other non-biological examples of codes, so what? There aren't any non-biological examples of turds, either, but that doesn't mean whenever I see a turd, I think "that was intelligently designed". Why do you think your question was relevant to my posting?

Re Colson:Being a charitable sort, I'm prepared to believe that people can make serious mistakes, and later admit their wrong, regret it, reform, and by changed conduct redeem themselves. I'm even willing to grant that religious conversion might sometimes play a role in such a reform.

However, having read some of Colson's output "Anno Domini", I say that he's still a liar. He's just lying for a different Commander In Chief is all.

About Charles Colson...it's true that he was a criminal in his "former life", but he found Jesus while he was in jail and claims to have rehabilated himself. I guess the charitable thing to do is believe him; certainly he hasn't been arrested for anything since then. All of this is probably worth a mention.

But his radio program is more about Christian Evangelism than Information Theory. Not that there's anything wrong with that...if I were a publisher and Ms. Pearcy came to me with a book about Christian Evangelism, I'd look at her resume and agree that she had solid qualifications to write it.

But she doesn't seem to have any kind of background in Information Theory, and people who work in the field seem to agree that she doesn't understand it very well. What was her publisher thinking???

They were thinking: "Here's an apologetics book that will appeal to our target market, which is Evangelical Christians. So let's run with it". What makes you think the publisher knows any more about info-theory than the authors do? Or has the motivation to have the MS vetted by someone who does? All kinds of crap gets printed by religious publishing houses (and to be fair: by lots of non-religious publishers, too).

That leads to "Sturgeon's Law", that "90% of everything is crud." Of course, there's a tale there. Briefly, Theodore Sturgeon at an SF conference listened to a literary critic pronounce that "90% of science fiction is crud." At the time for comments, Sturgeon responded, "Sure, 90% of science fiction is crud. But 90% of everything is crud."

"So I left the library, disillusioned. How could the creationists be so wrong? Could they have allowed their personal religious beliefs to get in the way of their understanding? Or could they be deliberately misinforming the public to support their evangelical goals? No, the answer is clear: all the experts in information theory must be suppressing the truth."

Or, they could make an extraordinarily common mistake. Many people -- including scientists -- make the mistake that random equals purposeless. Kenneth Miller made this mistake in his Biology textbook until it was brought to his attention in 1995 at a meeting of the ASA. This brought about entertaining theater at Dover where the defendents' attorney tried to only refer to the ten-year-old edition and not the present corrected one. So, was Kenneth Miller suppressing the truth ten years ago? No, he just made a common error just like Pearcey.

Information theory can be very counterintuitive. For example, injecting noise into a bidirectional quantum channel increases its capacity. Or, for what we are discussing here the highest communication rate is produced by a random code (at least classically as this falls apart for quantum channels).

The counterintuitive nature of information theory can explain why a layman like Pearcey makes an error. When you have "experts" such as Dembsky making arguments that sound correct but are wrong it is no wonder that many people can be lead astray by it.

While I realize "teaching the controversy" was tongue in cheek, it would really be helpful here. Evolution as purposeless is a common misperception because so many people believe random equals purposeless. Information theory can help allay this misperception.

“(Afterall, the sequence "ACGGCT" has no inherent usefulness unless you define the translation system and know the biology of the animal that will use(it) the resulting protein; a different translation system or different animal might render the sequence useless.)# posted by BC : 3:37 PM “

Here is where you go off the rails. You are no longer asking about "information" (as the term is used in info-theory), but about the meaning of the string. Meaning depends on a knowledge of context (memory address, CPU opcode, binary dump of text, etc....), and it's also (AFAIK) not formally, mathematically defined. (I would claim that meanings are largely culturally-dependent artefacts of human minds). Among other things, this implies that you cannot make statements about what random mutation can or cannot do to the "meaning" of a string -- since you haven't quantified the amount of "meaning" you had to start with, you've no basis for saying it's now more or less than it was (and it's even less obvious what the "meaning" of DNA is w.r.t. phenotype or fitness).

Let's be clear what the Creationist rhetoric is here: they are trying to use info-theory to pose a mathematically air-tight knock-down refutation of evolution. In so doing they invariably commit one of both of the following fallacies:

1) Getting the info-theory just plain wrong (as Pearcey does).2) Equivocating between the formal definition of "information" and its natural-language usage, which is closer to "meaning".

They should be nailed to the wall hard and fast every single time they do this.

The question of whether information is in "the eye of the beholder" or not is a little bit subtle. The problem with defining complexity of an object as the length of the shortest description of that object is that it depends on what primitives you have. Turing machines have certain primitive operations (read a square, write a square, move left, move right, halt) and arithmetic has certain other primitives (add, multiply, increment, decrement, test for equality). The precise number you get for the complexity of some pattern depends on which set of primitives you choose.

Entropy is in a similar boat. The information-theoretic definition of entropy is this:

The entropy of macrostate S is proportional to the log of the number of microstates that produce the same macrostate.

So to measure entropy, you have to use some criterion for when two different microscopic states are "the same" macroscopically. This depends on which features of the macroscopic state you consider to be important. For a gas, the common parameters are: Total energy, volume, number of molecules, total momentum, total angular momentum, total charge, etc.

However, the interesting thing about information theory is that even though the precise value for information content is subjective (since it depends on a choice of primitives), in practice, it doesn't make much difference which primitives you choose. So in practice, information is approximately objective.

"First, let's clarify what you mean by "code". To a mathematician, a code is a set of words S such that any word that can be written as a product of words in S only has one such representation. In other words, there is unique decipherability. Thus the set {a, ab} is a code, but {a, ab, ba} is not, since aba can be factored as (ab)(a) or (a)(ba).

Given that, is DNA a code? No, because codes are sets of words, and DNA is a molecule. When we interpret DNA as a string of symbols, that is our interpretation. Maybe the proper way to think of DNA is something entirely different, let's say, something involving topology."

Respectfully, Prof. Shallit, you dodged my question in two ways:

1. You introduced an arcane narrow definition of code from mathematics, and then some other definitions in different contexts.

In the April 2004 edition of Scientific American, the authors Freeland & Hurst published their article entitled: "Evolution Encoded: New discoveries about the rules governing how genes encode proteins have revealed nature's sophisticated 'programming' for protecting life from catastrophic errors while accelerating evolution" (Page 84)

Further, the authors note that "three-letter sequences, or codons, of DNA and RNA encode the individual amino acids that build and maintain all life on earth." (Page 84) Throughout their article they use the term "code" to refer to DNA and genetic processes.

On page 87, they discuss the "decoding rules" for genetic materials.

I guess either they are clueless hacks (trolls like me?) -- or your definitions are not the only ones used. Those science authors think they are dealing with encoded information that is decoded to produce effects in cells, and they use the term "code" without apology.

2. You did not address my question, which asked about the material forces, outside of biology-derived processes, that create codes along with the encoding and decoding devices that use the codes.

The ice core example you gave could, being generous to your assumptions, suggest an encoding process. Where is the non-biology-derived *decoder*?

Shining the light as you suggest, is an action taken by a biological being or something created by a biological being. I'm looking for the purely material, non-biological example of a decoder.

If you ask a mathematician what a code is, don't be surprised if you get a mathematical definition.

I agree that the word "code" can be used in different ways. Why don't you tell me what your definition is, before asking me to produce examples?

As for my example, light shining on ridges doesn't necessarily imply any biological being. Or haven't you seen the sun lately?

I still don't see your point. Everybody agrees that biology results in special behavior. If your goal is to produce something about biology we don't see elsewhere in the universe, you could have said "Where else do we see imperfect replication going on for billions of years?"

I appreciated the discussion in this post. As someone new to information theory, I do have a question about one of the final points you made, that high information content is evidence for random production. Would that also hold true with a lengthy work of literature? Is the amount of information in an Agatha Christie novel evidence of random production? Of course, there's far less information in a novel than in a strand of DNA, so is there a point at which increasing amounts of information begin to point to randomness rather than deliberate order?

Thanks so much for your help, and again, thanks for the thoughtful post!

Would that also hold true with a lengthy work of literature? Is the amount of information in an Agatha Christie novel evidence of random production?

Yes, I'd say so. Ultimately, random interactions are responsible for much of everyday activity, and creativity is probably a process of "generate-and-test", where the "generate" part is a random process.